Heat a medium skillet over moderately high heat. Add a large handful of spinach and cook, stirring, until the leaves are wilted. Transfer the wilted spinach to a colander and repeat with the remaining leaves. Gently squeeze the spinach dry, coarsely chop and reserve.
In the same skillet, heat 1 tablespoon of olive oil. Add the red onion and cook over moderate heat until softened, about 7 minutes. Transfer the onion to a large bowl and let cool.
Add the ground lamb to the bowl with the onions and break it up slightly. Add the red wine, cumin, cinnamon, 1/2 teaspoon of salt and 1/2 teaspoon of black pepper and blend well. Gently form the mixture into four 4-inch patties.
In the same skillet, heat the remaining 2 tablespoons of olive oil. Add the minced garlic and cook over moderate heat until fragrant, about 40 seconds. Add the wilted spinach and cook, stirring, until hot. Season the spinach with salt and pepper, cover and keep warm.
Lightly brush the bread with olive oil and cook on prepared grill, turning once, until lightly browned, about 1 minute per side. Spread the fresh goat cheese on the bread and top with the garlic-spinach mix.
Brush the lamb patties with olive oil and season lightly with salt and pepper. Grill over moderately high heat, turning once, until the patties are nicely charred outside and medium-rare within, about 4 minutes per side. Transfer the chopped lamb steaks to the bread, and serve with a fork and knife.